QUESTION 2 Represent the following on a number line: \( 2.1 \quad\{x: x \geq-50 ; x \in \mathrm{Z}\} \) \( 2.2 \quad(-10 ; 20] \)

To represent the given sets on a number line, we will illustrate each set separately. ### 2.1 \( \{x: x \geq -50 ; x \in \mathrm{Z}\} \) This set includes all integers \( x \) that are greater than or equal to \(-50\). - The number line will start at \(-50\) and extend to the right, including all integers from \(-50\) onward. - We will use a closed circle at \(-50\) to indicate that \(-50\) is included in the set, and we will mark the integers to the right. **Number Line Representation:** ``` <---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---> -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 ● ``` ### 2.2 \( (-10 ; 20] \) This set includes all real numbers \( x \) that are greater than \(-10\) and less than or equal to \(20\). - The number line will start just above \(-10\) (not including \(-10\)) and extend to \(20\) (including \(20\)). - We will use an open circle at \(-10\) to indicate that \(-10\) is not included, and a closed circle at \(20\) to indicate that \(20\) is included. **Number Line Representation:** ``` <---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---> -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 (-------------------● ``` In summary: - For \( 2.1 \), we have integers starting from \(-50\) and going to positive infinity. - For \( 2.2 \), we have all real numbers between \(-10\) (not included) and \(20\) (included).